1 / 16

Solutions to Nash Equilibrium Exercises

Solutions to Nash Equilibrium Exercises. NOTE: I have coloured payoffs green if they are the best response rather than underlining. A Nash equilibrium is therefore a square with two green payoffs. If you want to discuss these solutions, email me or see me in my office hour. GAME 1.

elgin
Télécharger la présentation

Solutions to Nash Equilibrium Exercises

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Solutions to Nash Equilibrium Exercises NOTE: I have coloured payoffs green if they are the best response rather than underlining. A Nash equilibrium is therefore a square with two green payoffs. If you want to discuss these solutions, email me or see me in my office hour.

  2. GAME 1 PLAYER TWO a b Nash Equilibrium at 1b2a. A is dominant strategy for 2. a 0 , 5 5 , 0 PLAYER ONE 4 , 4 1 , 1 b Confused? Click here for an animated explanation.

  3. GAME 2 PLAYER TWO a b Nash Equilibria at 1a2a and 1b2b. No dominant strategy. a 2 , 1 0 , 0 PLAYER ONE 0 , 0 1 , 2 b

  4. GAME 3 PLAYER TWO a b Nash Equilibria at 1a2a and 1b2b. A is weakly dominant strategy for 1. a 1 , 1 0 , 0 PLAYER ONE 0 , 1 0 , 2 b

  5. GAME 4 PLAYER TWO a b Nash Equilibria at 1a2a and 1b2b. No dominant strategy. a 2 , 1 0 , 0 PLAYER ONE 0 , 0 1 , 2 b

  6. GAME 5 PLAYER TWO a b Nash Equilibrium at 1b2a. B is dominant strategy for 1; A is dominant strategy for 2. a 5 , 9 5 , 4 PLAYER ONE 8 , 8 6 , 7 b

  7. GAME 6 PLAYER TWO a b Nash Equilibria at 1a2a and 1b2b. No dominant strategy. a 14 , 10 0 , 1 PLAYER ONE 2 , 1 1 , 2 b

  8. GAME 7 PLAYER TWO a b Nash Equilibriua at 1a2a and 1b2b. A is weakly dominant strategy for 1. a 1 , 3 0 , 2 PLAYER ONE 0 , 2 0 , 3 b

  9. GAME 8 PLAYER TWO a b Nash Equilibrium at 1b2b. B is dominant strategy for 2. a 5 , 0 1 , 1 PLAYER ONE 1 , 2 2 , 3 b

  10. GAME 9 PLAYER TWO a b Nash Equilibrium at 1b2a. A is dominant strategy for 2; B is dominant strategy for 1. a 17 , 40 20 , 30 PLAYER ONE 18 , 23 91 , 21 b

  11. GAME 10 PLAYER TWO a b Nash Equilibrium at 1b2b. B is dominant strategy for both 1 and 2. a 1 , 1 -1 , 4 PLAYER ONE 2 , 2 0 , 3 b

  12. GAME 1 PLAYER TWO a b LET’S BE PLAYER TWO. IF PLAYER ONE PLAYS “A” WE CAN EITHER PLAY “A” AND GET 5 OR WE CAN PLAY “B” AND GET 0 SO WE PLAY “A” a 0 , 5 0 , 5 5 , 0 PLAYER ONE 4 , 4 1 , 1 b

  13. GAME 1 PLAYER TWO a b WE’RE STILL PLAYER TWO, BUT... THIS TIME, IF PLAYER ONE PLAYS “B” WE CAN EITHER PLAY “A” AND GET 4 OR WE CAN PLAY “B” AND GET 1 SO WE PLAY “A” a 0 , 5 5 , 0 PLAYER ONE 4, 4 4 , 4 1 , 1 b

  14. GAME 1 PLAYER TWO a b NOW LET’S BE PLAYER ONE. IF PLAYER TWO PLAYS “A” WE CAN EITHER PLAY “A” AND GET 0 OR WE CAN PLAY “B” AND GET 4 SO WE PLAY “B” a 0 , 5 5 , 0 PLAYER ONE 4 , 4 4 , 4 1 , 1 b

  15. GAME 1 PLAYER TWO a b FINALLY, IF PLAYER TWO PLAYS “B” WE CAN EITHER PLAY “A” AND GET 5 OR WE CAN PLAY “B” AND GET 1 SO WE PLAY “A” a 0 , 5 5 , 0 5 , 0 PLAYER ONE 4 , 4 1 , 1 b

  16. GAME 1 A Nash Equilibrium is easy to spot – it’s where a square has two green payoffs. In this case, then, it is 1b2a. Is there a dominant strategy? Yes. If 1 plays “A”, 2 plays “A” And if 1 plays “B”, 2 plays “A” So A is a dominant strategy for 2. PLAYER TWO a b a 0 , 5 5 , 0 PLAYER ONE 4 , 4 1 , 1 b

More Related